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March 2012 An SIR epidemic model on a population with random network and household structure, and several types of individuals
Frank Ball, David Sirl
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Adv. in Appl. Probab. 44(1): 63-86 (March 2012). DOI: 10.1239/aap/1331216645

Abstract

We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own `household' and with their neighbours in a random graph representing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of individuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calculating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball, Sirl and Trapman (2009) heuristically motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results.

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Frank Ball. David Sirl. "An SIR epidemic model on a population with random network and household structure, and several types of individuals." Adv. in Appl. Probab. 44 (1) 63 - 86, March 2012. https://doi.org/10.1239/aap/1331216645

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1236.92043
MathSciNet: MR2951547
Digital Object Identifier: 10.1239/aap/1331216645

Subjects:
Primary: 92D30
Secondary: 05C80, 60J80

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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